Start by declaring international drinking rules
Beer pong:
2 teams of 2, 9 cups filled with beer each, 2 ping pong balls. Each team takes it in turns to throw the balls into the opponents cups, if you score, they have to down the cup. Spillage is lickage.
Arrogance:
A pack of cards is shuffled and the top card turned over. The idea is to guess whether the next card will be higher, or lower than the card most recently turned over. Each person has to 'bet' a portion of their drink depending on how confident they are by pouring it into a jug. If you get it wrong, you down whats in the jug, get it right and the next person continues the game.
Sexual animals (not sure if actual name):
Organise into small teams (needs a large group of people). Each team gives themself a team name such as "Randy Rhinoes", "Pedo penguins" etc.. along with an associated action. Every team stands up in turn to show action and say their team name. One team then starts the game by saying their team name and performing their action, then passes it on to someone else by saying their team name and performing their action. Your team drinks for hesitation, or getting a team name/action wrong.
Ring of fire - Usually played with:
Waterfall:
Everyone stands up and starts drinking, who can only stop drinking if you finish your drink, or the person to the left of you stops drinking. Only the person who originally drew the card can choose to stop drinking
20+1:
Start by giving a direction and saying either one, two or three numbers. saying two numbers reverses direction, three numbers skips one person. You are not allowed to say one number if the previous person has just said
one number etc.. Numbers must increase each time they are said. The person that has to say 21 has to down their drink
One Fat frog:
People stand up in turn saying "one" "fat" "frog" "jumped" "into" "the" "pond" "splash" along with the associated action. After a full rotation, two people must stand up both saying/performing in synchronisation, after another rotation three people must stand up for each word/action. If you get it wrong, you drink.
I have never:
You say I have never done something, if someone on the table (including youself) has done that action, they must drink.
Most likely to:
You declare something that someone is most likely to do. Everyone playing the game then votes on who they think is the most likely to do that thing. The person with the most votes has to drink.
Thumb master
The person who draws the this card is declared thumb master. At any time during the night they might put their right thumb on the table. At this point everyone else must also put their thumb on the table and hold it there, the last person to do so has to drink.
Eyes master:
If you make eye contact with eyes master, you have to drink.
Question master:
If you answer a question asked by question master, you have to drink.
Drinking buddy:
Declare someone your drinking buddy. Everytime you drink, they drink. (hint, try and form chains)
As well as other things such as god cards (Make one rule that everyone has to follow for the rest of the night), etc...
This is the witch:
Person 1: "Person 2, This is the witch"
Person 2: "The what?"
1: "The witch"
2: "Ahhh, the witch, Person 3, this is the witch"
3: "The what?"
2: "The what?"
1: "The witch"
2: "The witch"
3: "Ahhh, the witch, Person 4, this is the witch"
etc... Try and loop back to other people halfway through the chain for added complexity

Oh, if you get it wrong, you drink.
Also, if we have enough time, the LOTR drinking game. Rules are far too long to explain here, google it.
Theres also countless word association games, and many many others.